Characterization of the monotone polar of subdifferentials

Marc Lassonde (1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications

We show that a point is solution of the Minty variational inequality of subdifferential type for a given function if and only if the function is increasing along rays starting from that point. This provides a characterization of the monotone polar of subdifferentials of lower semicontinuous functions: it is a common subset of their graphs which depends only on the function.

Mots clés: lower semicontinuity; subdifferential; lower Dini subderivative; Minty variational inequality; increase-along-rays property; monotone polar; maximal monotonicity

Domaines: Optimisation et contrôle [math.OC]

Marc Lassonde. Characterization of the monotone polar of subdifferentials. Optimization Letters, 2013, pp.1-4. ⟨10.1007/s11590-013-0693-7⟩. ⟨hal-00842670⟩